Mitt Romney repeatedly used the term during the Republican primary campaign to talk about how his immigration enforcement policies would lead to unauthorized immigrants leaving the U.S. of their own accord, rather than needing to be deported.

"Using the word 'self-deportation' — it's a horrific comment to make," Priebus said, in a forceful rebuke. "I don't think it has anything to do with our party. When a candidate makes those comments, obviously, it hurts us."

Preibus spent much of a mid-afternoon session with reporters defending the party's progress with Latino voters and steps on immigration reform, which it made a priority five months ago in its touted Growth and Opportunity Project.

King is making life especially difficult for Priebus, five months into a GOP "rebrand" that depends on patching up relations with Latinos.

Priebus bristled when asked about King's comments on Thursday — specifically, one in which he said illegal immigrants have "calves the size of cantaloupes" so they can haul "75 pounds of marijuana across the desert."

"Well, of course, it's hurtful," Priebus said of those comments. "Of course, it hurts. ... Just, not good."

Priebus' comments to reporters came right after a program in which the RNC highlighted "Rising Stars" in the party: new faces that it will promote through media appearances. One of those stars was Marilinda Garcia, a New Hampshire State Rep. who wants a legislative fix to the nation's current immigration laws and touted new ways she thought Republicans should engage Latino voters.

APMarilinda Garcia

Though it wasn't a topic of any of the panels here, multiple state chairs and GOP officials openly talked about their support for comprehensive immigration reform — though they were skittish about supporting the Senate-passed bill.

"We have this stereotype of Republicans being old, white, Anglo-Saxon men. But there are people like me that have been out there working for years," said Garcia, 30. "So [Republicans] are like, 'Why not have her talk about our values instead of Newt Gingrich all the time?'"

Still, one of Priebus' remarks that promoted the GOP's message on immigration also gave a signal of how far it has to go.

"Everything's not 100%. I mean, I don't agree with my wife on 100% of the issues, and we've got a pretty good marriage," Priebus said.

"I think these are important issues. But you have to admit — the fact that the GOP is having a serious, high-level conversation about immigration reform is something that's very different. And it's something that we've embraced."